Line an 8×8 inch baking dish with parchment paper, allowing some extra parchment to hang over the sides for easy removal later.
Combine the granulated sugar, milk, and butter in a medium saucepan over medium heat. Stir continuously until the mixture comes to a rolling boil.
Once boiling, continue to cook and stir for about 4-5 minutes. The mixture should thicken slightly and the sugar should dissolve completely.
Remove the saucepan from heat and stir in the creamy peanut butter and vanilla extract until smooth and well combined.
Quickly add the caramel bits or pieces and (black sesame seeds if using) to the mixture, stirring until evenly distributed. The heat from the fudge will slightly melt the caramel, creating lovely pockets of gooey caramel throughout the fudge.
Pour the fudge mixture into the prepared baking dish, spreading it out evenly. Allow it to cool at room temperature for about 30 minutes.
Transfer the dish to the refrigerator and let it chill for at least 2 hours, or until fully set.
Once set, use the overhanging parchment paper to lift the fudge out of the pan. Cut into small squares and enjoy!